From the previous discussion we gather that the present universe is
matter dominated. The matter density is some 2 × 103
larger than the radiation density
((fossil radiation)
= 4.5 × 10-5
while (matter) =
0.1). However, as the energy density of a matter-dominated universe
decreases with T3 - while the dependance is in
T4 for a radiation
dominated universe - we conclude that both densities were equal when
the universe was some 2 × 103 times hotter, that is at
approximately 5 × 103 K. The density was (2 ×
103)3 larger. In these conditions the
hydrogen atoms were ionized and the cosmic fluid was opaque to its own
radiation. The fossil radiation observed by Penzias and Wilson is
believed to have been emitted at the moment of recombination of
hydrogen, approximately when the universe became matter-dominated.

To the question: how hot has the universe been in the past? we can
give a first answer in the following way. As beautifully confirmed by
the COBE satellite in march 90, the fossil radiation has, very
accurately, a thermal (Bose-Einstein) distribution of photon momenta.
In the present universe there are no known physical processes capable
of thermalizing a population of photons. We need to go back to
temperature of at least a few thousand degrees to find appropriate
physical conditions. Thus we may conclude that the existence of the
fossil radiation gives us strong indications that, in the past, the
universe has reached such temperatures.